### If you are given a conditional, do you know how to get the converse? or the inverse? Maybe the contrapositive? May you determine when a conclusion follows a set of statements, if it follows by Law of Syllogism, or by Law of Detachment?

### Throughout this lesson, you will have plenty of opportunities to learn how to setup conditionals, their converse, inverse, and contrapositive. You will be able to understand when a conclusion follows by Law of Detachment, or by Law of Syllogism. This lesson takes great care in highlighting the different parts of these conditionals, and presents in careful detail the flow of the involved thinking in reaching to the right conclusions. You won't be disappointed! One very useful feature throughout the lesson is that you are given the opportunity to solve very similar problems on the screen with the markers tools menu and your stylus.

** Lesson's Content **

** Lesson's Glossary **

**Biconditional **

A conditional and the converse of this need to be true, in which case "*if only if* " is used with the hypothesis and the conclusion of the conditional to make the biconditional.

**Conditional **

Refers to an "*if p then q*" statement.

**Contrapositive **

In a conditional statement "*if p then q*", the contrapositive is "*if not p then not q*", and always have the same truth value as the original conditional.

**Converse **

In a conditional statement "*if p then q*", the converse is "*if q then p*".

** Counterexample **

A particular instance that makes one statement false.

** Inverse **

A form of conditional; *"if not p, then not q"*.

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